Sometimes it may be as simple as changing the
oil! There are various reasons
oil can get contaminated, especially problematic is something like running to rich or a float sticking and flooding the engine. That dilutes the
oil and can often lead to that "puff of smoke" worry. Perhaps YOUR motor doesn't like a low viscosity
synthetic oil either? Some motors just don't, others are OK with it.
In tracking down a smoke issue, I'd be tempted to change or verify my existing oil was good AND I'd run something like 15-40 dinosaur oil just to see if that had any impact. If it gets better but still persists, kick it up a notch, go for a bottle of STP and see if that helps as well. Actually, I run a bottle of STP when I change oil regardless of any problems I may or may not be having (flat tappet cam).